This is the essence of the QCB: The exponent—the quantum
Chernoff information, \(\xi _{QCB}\) , or its inhomogeneous counterpart,
\(\bar{\xi }_{QCB}\) —controls the redundancy, see Refs. [1]}, [2]}
for additional discussion and results. For the pure c-maybe
model, this exponent is the same whether using Eq. (REF ),
Eq. (REF ), or Eq. (REF ). The quantum mutual
information also yields the same decay and redundancy in the good
decoherence limit, as it is the same as \(\chi \left(\check{\mathcal {S}}:\mathcal {F}\right)\) 
from Eq. (REF ) In order to apply Eq. (REF ) for the quantum
mutual information, one needs \({^{\sharp }}\hspace{-1.42262pt}\mathcal {E}\rightarrow \infty \) . As already mentioned
in a prior footnote, though, this will entail good decoherence provided
some finite interaction between \(\mathcal {S}\)  and \(\mathcal {E}\)  components has taken
place.. In other words, all the information theoretic quantities provide
the same decay and redundancy, which the asymptotic calculation, Eq.
(REF ), makes apparent in a non-empirical manner.
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